The paper discusses a possibility that a multiplicity of mind
phenomena can be understood from few fundamental principles of the mind
organization, which are mathematically formulated. The paper discusses the role
of concepts and emotions in the information processing by the mind and
identifies an “elementary thought process” in which an event (in the outside
world, or inside the mind) is understood as a concept. Previous attempts in
artificial intelligence at describing thought processes are briefly reviewed
and their fundamental (mathematical) limitations are discussed. The role of emotional
signals in overcoming these past limitations is emphasized. An elementary
thought process is related to semiotical notions of signs and symbols. It is
further related to understanding, imagination, intuition, and to the role of
aesthetic emotions and beauty in functioning of the mind. Relationships between
the mind and brain are briefly discussed. All the discussed notions are
grounded in psychological data and mathematical theory, yet knowledge of
mathematics is not assumed, discussions related to the mathematical theory are
given conceptually, and the paper is accessible to non-mathematicians. A theory
described here could possibly serve as a prolegomenon to a physical theory of
mind.

After creating a physical theory of the material world
Newton devoted his life to developing a science of the mind, the physics of
spiritual substance (Westfall 1983). Newton failed at his second project and
many contemporary physicists are still afraid to look at mind as a physical
system. This paper is an attempt to overcome this timidity and to demonstrate
that many of the mind phenomena can be explained from a few basic principles
that can be mathematically formulated, which is the essence of the physical
theory. Words like mind, thought,
imagination, emotion, concept, aesthetics, beauty are not often encountered
alongside physics or mathematics. People use these words in
many ways colloquially, but their use in science and especially in mathematics
of intelligence has not been uniquely defined and is a subject of active
research and ongoing debates[1]. According to a dictionary (AHCD), mind includes conscious and
unconscious processes, especially thought, perception, emotion, will, memory,
and imagination, and it originates in brain. These constituent notions will be
discussed throughout the paper.

A broad range of opinions exists on the mathematical
methods suitable for the description of the mind. Founders of artificial
intelligence thought that formal logic was sufficient
(Newell 1983) and no specific mathematical techniques would be needed to
describe the mind (Minsky 1988). An opposite point of
view is that there are few specific mathematical constructs, “the first
principles” of mind. Among researchers taking this view is Grossberg, who
suggested that the first principles include a resonant matching between
lower-level signals (Grossberg 1988) and higher-level
representations and emotional evaluation of conceptual contents (Grossberg and Levine 1987); Josephson, Meystel, Zadeh,
and the author suggested specific principles of the mind organization
(Josephson 1997; Meystel 1995; Zadeh 1997; Perlovsky 2001) [2]
. Hameroff, Penrose, and the author (among others) considered quantum
computational processes that might take place in the brain (Hameroff 1994;
Penrose 1994; Perlovsky 2001).
Although, it was suggested that new unknown yet physical phenomena will
have to be accounted for explaining the working of the mind (Josephson 1997; Penrose
1994). This paper describes mechanisms of mind that can be “implemented” by
classical-physics mechanisms of the brain neural networks.

Understanding signals coming from sensory organs involves
associating subsets of signals corresponding to particular objects with
internal representations of these objects. This leads to recognition of the
objects and activates internal brain signals leading to mental and behavioral
responses that constitute the understanding of the meaning (of the objects).

Developing mathematical descriptions of the very
first recognition step of this seemingly
simple association-recognition-understanding process has not been easy, a
number of difficulties have been encountered during the past fifty years. These
difficulties have been summarized under the term combinatorial complexity (CC)
(Perlovsky 2001). The problem
was first identified in pattern recognition and classification problems in the
1960s and was named “the curse of dimensionality” (Bellman 1961). The following thirty years of developing adaptive statistical pattern
recognition and neural network algorithms designed for self-learning led to a
conclusion that these approaches often encountered CC of learning requirements: recognition of any object, it seemed, could
be learned if “enough” training examples could be used for an algorithm
self-learning. The required examples had to account for all possible variations
of “an object”, in all possible geometric positions, in all combinations with
other objects, sources of light, etc., leading to astronomical numbers of
required examples. By the end of the 1960s a different paradigm became popular:
rule-based systems (or expert systems) were proposed to solve the problem of
learning complexity. An initial idea was that rules would capture the required
knowledge and eliminate a need for learning. Rule systems work well when all
aspects of the problem can be predetermined. However, rule systems and expert
systems in the presence of unexpected variability, encountered CC of rules: more and more detailed
sub-rules and sub-sub-rules had to be specified. In 1980s model-based systems
became popular, which were proposed to combine advantages of adaptivity and
rules by utilizing adaptive models, but they encountered computational CC (N and NP complete algorithms). The CC became a
ubiquitous feature of intelligent algorithms and seemingly, a fundamental
mathematical limitation. The reason was that considered algorithms had to
evaluate multiple combinations of elements and the number of combinations is
very large: say, take 100 elements (not too large a number), but the number of
combinations of 100 elements is 100100, a number larger than the
number of elementary particles in a Universe, and no computer would ever be
able to compute that many combinations.

Combinatorial
complexity has been related to the type of logic, underlying various algorithms
and neural networks (Perlovsky 1998a). Formal logic is based on the “law of
excluded third”, according to which every statement is either true or false and
nothing in between. Therefore, algorithms based on formal logic have to
evaluate every little variation in data or internal representations as a
separate logical statement; a large number of combinations of these variations
causes combinatorial complexity. In fact, combinatorial complexity of
algorithms based on logic has been related to the Gödel theory: it is a
manifestation of the incompleteness of logic in finite systems (Perlovsky
1996a). Multivalued logic and fuzzy
logic were proposed to overcome limitations related to the law of excluded
third (Jang et al 1996). Yet the
mathematics of multivalued logic is no different in principle from formal
logic. Fuzzy logic encountered a difficulty related to the degree of fuzziness:
if too much fuzziness is specified, the solution does not achieve a needed
accuracy, if too little, it might become similar to formal logic.

The
seemingly fundamental nature of the mathematical difficulties discussed above
led many to believe that classical physics cannot explain the working of the
mind. Yet, I would like to emphasize another aspect of the problem: often
mathematical theories of the mind were proposed before the necessary physical
intuition of how the mind works was developed. Newton, as often mentioned, did
not consider himself as evaluating various hypothesis about the working of the
material world, he felt that he possessed an intuition (Westfall 1983), or what we call today a
physical intuition about the world. A particular intuition about the mind is
that it operates with emotions. An essential role of emotions in the working of
the mind was analyzed from the psychological and neural perspective by
Grossberg (1987) from the neuro-physiological
perspective by Damasio (1995) and from the learning and control perspective by
the author (Perlovsky 1998b, 1999). One reason for
the engineering community being slow in adopting these results is the cultural
bias against emotions as a part of thinking processes. Plato and Aristotle
thought that emotions are “bad” for intelligence, this is a part of our
cultural heritage, and the founders of Artificial Intelligence repeated it.
Yet, as discussed in the next section, combining conceptual understanding with
emotional evaluations might be crucial for overcoming the combinatorial complexity
as well as the related difficulties of logic.

Let
me summarize briefly and in the most simplified way several aspects of the
working of the mind as it is understood today, which might be crucial to the
development of the theory of the mind. Mind emerged in evolution for the
purpose of survival and therefore it serves for a better satisfaction of the
basic instincts, which emerged as survival mechanisms even before mind.
Instincts operate like internal sensors: for example, when the sugar level in
the blood goes below a certain level an instinct “tells us” to eat. That which
is most accessible to our consciousness mechanism of the mind, are concepts:
the mind operates with concepts. Concepts are like internal models of the
objects and situations.

What
is the relationship between instincts and concepts and what is the mechanism
relating them? An ability for concepts evolved for instinct satisfaction and emotions
are neuronal signals connecting instinctual and conceptual brain regions.
Whereas in colloquial usage, emotions are often related to facial expressions,
higher voice pitch, exaggerated gesticulation — these are the outward signs of
emotions, serving for communication. A more fundamental role of emotions within
the mind system is that emotional signals evaluate concepts for the purpose of
instinct satisfaction. This evaluation is not according to rules or concepts
(as in rule-systems of artificial intelligence), but according to a different
instinctual-emotional mechanism described in the next section. This emotional
mechanism is crucial for breaking out of the “vicious circle” of combinatorial
complexity.

The
result of conceptual-emotional understanding of the world are actions (or behavior)
in the outside world or within the mind. In this paper we touch on only one
type of behavior, the behavior of improving understanding and knowledge about
the world (and self). In the next section we describe in notional terms with a
minimum of mathematics, a mathematical theory of a “simple”
conceptual-emotional recognition and understanding. As we will discuss, in
addition to concepts and emotions, it involves with necessity mechanisms of
intuition, imagination, conscious, unconscious, and aesthetic emotion. And this
process is intimately connected to an ability of mind to form symbols and interpret
signs.

Mind
involves a hierarchy of multiple levels of concept-models, from simple
perceptual elements (like an edge, or a moving dot), to concept-models of
object, to complex scenes, and up the hierarchy toward the concept-models of
the meaning of life and purpose of our existence. Hence the tremendous
complexity of the mind, yet relatively few basic principles of the mind
organization go a long way explaining this system.

Modeling field theory (Perlovsky 2001), (summarized below,
associates lower-level signals with higher-level concept-models (or internal
representations), resulting in an understanding of signals, while overcoming
the difficulties of CC described in Section 2. It is achieved by using measures
of similarity between the concept-models and the input signals combined with a
new type of logic, the fuzzy dynamic logic. Modeling field theory is a
multi-level, hetero-hierarchical system. This section describes a basic
mechanism of interaction between two adjacent hierarchical levels of signals
(fields of neural activation); sometimes, it will be more convenient to talk
about these two signal-levels as an input to and output from a (single)
processing-level.

At each level, the output are concepts recognized
(or formed) in input signals. Input signals X are associated with (or recognized, or grouped into) concepts
according to the representations-models and similarity measures at this level.
In the process of association-recognition, models are adapted for better
representation of the input signals; and similarity measures are adapted so
that their fuzziness is matched to the model uncertainty. The initial
uncertainty of models is high and so is the fuzziness of the similarity
measure; in the process of learning models become more accurate and the
similarity measure more crisp, the value of the similarity increases. I call
this mechanism fuzzy dynamic logic. Let me repeat again: knowledge of
mathematics is not required to read the following, the mathematical equations
given below could be just skipped, their meanings are explained in plain
language.

During the learning process, new associations of input
signals are formed resulting in the evolution of new concepts. Input signals {X(n)}, is a field of input neuronal synapse
activation levels, n enumerates the input neurons and X(n) are the activation levels; a set of concept-models {h} is
characterized by the models (representations) {Mh(n)} of the
signals X(n); each model depends on
its parameters {Sh}. In a highly simplified
description of a visual cortex, n enumerates the visual cortex neurons, X(n) are the “bottom-up” activation
levels of these neurons coming from the retina through visual nerve, and Mh(n)
are the “top-down” activation levels (or priming) of the visual cortex neurons
from previously learned object-models[3].
The learning process attempts to “match” these top-down and bottom-up activations
by selecting “best” models and their parameters. Mathematically, learning
increases a similarity measure between the sets of models and signals, L({X(n)},{Mh(n)}). The
similarity measure is a function of model parameters and associations between the
input synapses and concepts-models. It is constructed in such a way that any of
a large number of objects can be recognized, no matter if they appear on the
left or on the right. Correspondingly, a similarity measure is designed so that
it treats each concept-model as an alternative for each subset of signals

L({X},{M}) = r(h) l(X(n) | Mh(n));
(1)

here l(X(n)|Mh(n))
(or simply l(n|h)) is a conditional partial similarity between one signal X(n) and one model Mh(n), and
all possible combinations of signals and models are accounted for in this
expression. Parameters r(h) are proportional to the number of signals {n}
associated with the model h.

In the process of learning, concept-models are
constantly modified. From time to time a system forms a new concept, while
retaining an old one as well; alternatively, old concepts are sometimes
merged. [Formation of new concepts and
merging of old ones require a modification of the similarity measure (1); the
reason is that more models always result in a better fit between the models and
data. This is a well known problem, it can be addressed by reducing (1) using a
“penalty function”, p(N,M) that grows with the number of models M, and this
growth is steeper for a smaller amount of data N. For example, an
asymptotically unbiased maximum likelihood estimation leads to multiplicative
p(N,M) = exp(-Npar/2), where Npar is a total number of
adaptive parameters in all models (this penalty function is known as Akaike
Information Criterion, see (Perlovsky 2001) for further discussion and
references)].

The learning process consists in estimating model
parameters Sh and associating subsets of signals
with concepts by maximizing the similarity (1). Note, that (1) contains a large
number of combinations of models and signals, a total of HN items;
this was a cause for the combinatorial complexity of the past algorithms
discussed previously.

These variables
give a measure of correspondence between a signal X(n) and a model Mh relative to all other models, h’.
A mechanism, an internal dynamics, of the Modeling Fields (MF) is defined as
follows,

here dhh' is 1 if h=h', 0 otherwise.
Parameter t is the time of the internal dynamics of the MF system (like a
number of internal iterations). The following theorem was proven.

Theorem.
Equations (2) through (4) define a convergent dynamic system MF with stationary
states defined by max{Sh}L.

In plain language this means that the above
equations indeed result in concept-models in the “mind” of the MFT system,
which are most similar [in terms of similarity (1)] to the sensory data.
Despite a combinatorially large number of items in (1), a computational
complexity of the MF method is relatively low, it is linear in N, it could be
implemented by a physical system (like the brain) and therefore it may correspond
to the working of the mind. These equations describe a closed loop system,
which is illustrated in the block-diagram in Fig. 1. A reference to the closed loop emphasizes that the loop can
sustain its operations on its own, the loop is not entirely closed in that
there are input data into the loop and output concepts from the loop.

Figure 1:
For a single level of MFT, input signals are unstructured data {X(n)} and
output signals are recognized or formed concepts {h}. The MFT equations (2)
through (4) describe a continuous closed-loop operation involving input data,
similarity measures, models, and actions of the model adaptation.

The previous sub-section described a single processing
layer in a hierarchical MFT system. An input to each layer is a set of signals X(n), or in neural terminology, an
input field of neuronal activations. An output are the activated models Mh(Sh,n); it is a set of models or concepts recognized in
the input signals. Equations (2-4) describe a loop-process: at each iteration
(or internal-time t) the l.h.s. of the equations contain association variables
f(h|n) and other model parameters computed at the previous iteration. In other
words, the output models “act” upon the input to produce a “refined” output
models (at the next iteration). This process is directed at increasing the
similarity between the models and signals. It can be described as an internal
behavior generated by the models.

The output models initiate other actions as well.
First, activated models (neuronal axons) serve as input signals to the next
processing layer, where more general concept-models are recognized or created.
Second, concept-models along with the corresponding instinctual signals and
emotions may activate behavioral models and generate behavior directed into the
outside world (a process not contained within the above equations). In general,
a higher level in a hierarchical system provides a feedback input into a lower
level. For example, sensitivity of retinal ganglion cells depends on the
objects and situations recognized higher up in the visual cortex; or a gaze is
directed based on which objects are recognized in the field of view. More
complete interactions within this hierarchical organization are illustrated in
Fig.2.

Figure 2:
More details of integrated interactions are shown for a single-level loop of
MFT at the bottom of the hierarchy: input data X(n) are coming from the outside
world through sensors; sensors and effectors are acting in the surrounding
world based on the results of information processing inside the MFT system.

Concept-objects identified at the output of the
lower level of MFT system in Fig.2 become input signals to the next MFT level
which identifies more general concepts of relationships among objects and
situations; at the same time more general concepts of understanding identified
at a higher level activate behavioral concept-models that affect processes at a
lower level. The agent processes, or the loop-processes of model-concept
adaptation, understanding and behavior generation continue up and down the
hierarchy of the MFT levels.

The loop of operations of MFT can be better
described as multiple loops each involving a model; to some extent these
multiple loops are independent, yet some models interact when they are
associated with the same data pieces. Therefore MFT is an intelligent system
composed of multiple adaptive intelligent agents which possess a degree of
autonomy yet interact among themselves. Each concept-model along with the
similarity measure and behavioral response is a continuous loop of operations,
interacting with other agents from time to time; an agent is "dormant"
until activated by a high similarity value. When activated, it is adapted to
the signals and other agents, so that the similarity increases. Every piece of
signal may activate several concepts, or agents, in this way data provide
evidence for the presence of various objects (or concepts). Agents compete with
each other for evidence (data), while adapting to the new signals.

Equations (2-4) describe an elementary process of
perception or cognition, in which a large number of model-concepts compete for
incoming signals, model-concepts are modified and new ones are formed, and
eventually, more or less definite connections [high or low values of f(h|n),
varying between 0 and 1] are established among signal subsets on the one hand,
and model-concepts on the other. Perception refers to processes in which the
input signals come from sensory organs and model-concepts correspond to objects
in the surrounding world. Cognition refers to higher levels in the hierarchy
where the input signals are concepts activated at lower levels and
model-concepts are more complex and correspond to situations and relationships
among lower-level concepts.

A salient mathematical property of this processes
ensuring a smooth convergence is a correspondence between uncertainty in models
(that is, in the knowledge of model parameters) and uncertainty in associations
f(h|n). In perception, as long as model parameters do not correspond to actual
objects, there is no match between models and signals; many models poorly match
many objects, and associations remain fuzzy (nor 1 nor 0). Eventually, one
model (h') wins a competition for a subset {n'} of input signals X(n), when parameter values match
object properties, and f(h'|n) values become close to 1 for nÎ{n'}
and 0 for nÏ{n'}.
This means that this subset of data is recognized as a specific object
(concept). Upon the convergence, the entire set of input signals {n} is divided
into subsets, each associated with one model-object, uncertainties become
small, and fuzzy a priori concepts become crisp concepts. Cognition is different
from perception in that models are more general, more abstract, and input
signals are the activation signals from concepts identified (cognized) at a
lower hierarchical level; the general mathematical laws of cognition and
perception are similar in MFT and constitute a basic principle of the mind
organization. Let us discuss relationships between the MFT theory and concepts
of mind developed in psychology, philosophy, linguistics, aesthetics,
neuro-physiology, neural networks, artificial intelligence, pattern
recognition, and intelligent systems.

A “minimal” subset of these processes has to involve
mechanisms for afferent and efferent signals, (Grossberg, 1988), in other
words, bottom-up and top-down signals coming from outside (external sensor
signals) and from inside (internal representation signals). According to
Carpenter and Grossberg (1987) every recognition and concept formation process
involves a “resonance” between these two types of signals. In MFT, at every
level in a hierarchy the afferent signals are represented by the input signal
field X, and the efferent signals
are represented by the modeling field signals Mh; resonances correspond
to high similarity measures l(n|h) for some subsets of {n} that are
“recognized” as concepts (or objects) h. The mechanism leading to the
resonances is given by (2-4), and we call it an elementary thought-process. The
elementary thought-process involves elements of conscious and unconscious
processes, imagination, memory, internal representations, concepts, instincts,
emotions, understanding and behavior as further described later.

A description of working of the mind as given by the
MFT dynamics was first provided by Aristotle, describing thinking as a learning
process in which an a priori form-as-potentiality (fuzzy model) meets matter
(sensory signals) and becomes a form-as-actuality (a concept). Jung suggested
that conscious concepts are developed by mind based on genetically inherited
structures of mind, archetypes, which are inaccessible to consciousness (1934) and Grossberg (1988) suggested that
only signals and models attaining a resonant state (that is signals matching
models) reach consciousness.

In the elementary thought process, subsets in the incoming
signals are associated with recognized model-objects, creating phenomena (of the MFT-mind) which are understood as objects, in other words signal subsets acquire meaning (e.g., a subset of retinal
signals acquires a meaning of a chair). There are several aspects to
understanding and meaning. First, object-models are connected (by emotional
signals: Grossberg and Levine 1987, Perlovsky 2001; Perlovsky 1998b) to
instincts that they might satisfy, and also to behavioral models that can make
use of them for instinct satisfaction. Second, an object is understood in the
context of a more general situation in the next layer consisting of more
general concept-models, which accepts as input-signals the results of object
recognition. That is, each recognized object-model (phenomenon) sends (in
neural terminology, activates) an output signal; and a set of these signals
comprises input signals for the next layer models, which ‘cognize’ more general
concept-models. And this process continues up and up the hierarchy of models
and mind toward the most general models a system could come up with, such as
models of universe (scientific theories), models of self (psychological
concepts), models of the meaning of existence (philosophical concepts), models
of a priori transcendent intelligent subjects (theological concepts).

Imagination involves excitation of a neural pattern in a
visual cortex in the absence of an actual sensory stimulation (say, with closed
eyes) (Grossberg 1988). Imagination was often considered to be a part of
thinking processes; Kant (1790)
emphasized the role of imagination in the thought process, he called thinking
“a play of cognitive functions of imagination and understanding”. Whereas the
pattern recognition and artificial intelligence algorithms of the recent past
would not know how to relate to this
(Newell 1983; Minsky 1988), the Carpenter and Grossberg resonance model
(1987) and the MFT dynamics both describe imagination as an inseparable part of
thinking: imagined patterns are top-down signals that prime the percepting cortex areas (priming is a neural terminology for making neural cells to be more
readily excited). In MFT, the imagined neural patterns are given by models Mh.
MFT (in agreement with neural data) just adds details to Kantian description:
thinking is a play of higher-hierarchical-level
imagination and lower-level
understanding. Kant identified this “play” [described by (3-6) or (7-12)] as a
source of aesthetic emotion; modeling aesthetic emotion in MFT is described
later.

Historically, the mind is described in psychological and
philosophical terms, whereas the brain is described in terms of neurobiology
and medicine. Within scientific exploration the mind and brain are different
description levels of the same system. Establishing relationships between these
description is of great scientific interest. Today we approach solutions to
this challenge (Grossberg 2000), which
eluded Newton in his attempt to establish physics of “spiritual substance”(Westfall
1983). General neural mechanisms of the elementary thought process (which are
similar in MFT and ART (Carpenter and Grossberg, 1987) have been confirmed by
neural and psychological experiments, this includes neural mechanisms for
bottom-up (sensory) signals, top-down “imagination” model-signals, and the
resonant matching between the two
(Grossberg 1988; Zeki 1993; Freeman 1975). Adaptive modeling abilities
are well studied with adaptive parameters identified with synaptic connections
(Koch and Segev 1998; Hebb 1949); instinctual learning mechanisms have been
studied in psychology and linguistics (Piaget 2000; Chomsky 1981; Jackendoff
2002; Deacon 1998).

Functioning of the mind and brain cannot be understood in
isolation from the system’s “bodily needs”. For example, a biological system
(and any autonomous system) needs to replenish its energy resources (eat); this
and other fundamental unconditional needs are indicated to the system by
instincts, which could be described as internal sensors. Emotional signals,
generated by this instinct are perceived by consciousness as “hunger”, and they
activate behavioral models related to food searching and eating. In this paper
we are concerned primarily with the behavior of recognition: instinctual
influence on recognition modify the object-perception process (3) - (6) in such
a way, that desired objects “get” enhanced recognition. It can be accomplished
by modifying priors, r(h), according to the degree to which an object of type h
can satisfy a particular instinct. Details of these mechanisms are not
considered here, except for a specific instinct considered below.

Recognizing objects in the environment and understanding
their meaning is so important for human evolutionary success that there has
evolved an instinct for learning and improving concept-models. This instinct
(for knowledge and learning) is described in MFT by maximization of similarity
between the models and the world, (1). Emotions related to
satisfaction-dissatisfaction of this instinct are perceived by us as
harmony-disharmony (between our understanding of how things ought to be and how
they actually are in the surrounding world). According to Kant (1790) these are aesthetic emotions (emotions that are
not related directly to satisfaction or dissatisfaction of bodily needs).

Intuitionincludes
an intuitive perception (imagination) of object-models and their relationships
with objects in the world, as well as higher-level models of relationships
among simpler models. Intuition involves fuzzy unconscious concept-models,
which are in a state of being learned and being adapted toward crisp and
conscious models (a theory); such models may satisfy or dissatisfy the
knowledge instinct in varying degrees before they are accessible to
consciousness, hence the complex emotional feel of an intuition. The beauty of a physical theory discussed
often by physicists is related to satisfying our feeling of purpose in the
world, that is, satisfying our need to improve the models of the meaning in our
understanding of the universe.

Beauty.
Harmony is an elementary aesthetic emotion related to improvement of
object-models. Higher aesthetic emotions are related to the development of more
complex “higher” models: we perceive an object or situation as aesthetically
pleasing if it satisfies our learning instinct, that is the need for improving
the models and increasing similarity (1). The highest forms of aesthetic
emotion are related to the most general and most important models. According to
Kantian analysis, among the highest models are models of the meaning of our
existence, of our purposiveness or intentionality, and beauty is related to
improving these models: we perceive an object or a situation as beautiful, when
it stimulates improvement of these highest models of meaning. Beautiful is what
“reminds” us of our purposiveness.

The general neural mechanisms of the elementary thought
process, which includes neural mechanisms for bottom-up (sensory) signals,
top-down “imagination” model-signals, and the resonant matching between the two
(Grossberg 1988; Zeki 1993; Freeman 1975), have been confirmed by neural and
psychological experiments (these mechanisms are similar in MFT and ART,
Carpenter and Grossberg, 1987). Adaptive modeling abilities are well studied
and adaptive parameters have been identified with synaptic connections (Koch
and Segev 1998; Hebb 1949); instinctual learning mechanisms have been studied
in psychology and linguistics (Piaget 2000; Chomsky 1981). Ongoing and future
research will confirm, disprove, or suggest modifications to specific
mechanisms of model parameterization and parameter adaptation (5) or (8), reduction
of fuzziness during learning (9), similarity measure (1) as a foundation of aesthetic
instinct for knowledge, relationships between psychological and neural mechanisms
of learning on the one hand and, on the other, aesthetic feelings of harmony
and emotion of beautiful. Differentiated forms of (1) need to be developed for
various forms of the knowledge instinct (child development, language learning,
etc.) Future experimental research needs to study in details the nature of
hierarchical interactions: to what extent the hierarchy is “hardwired” vs.
adaptively emerging; what is a hierarchy of learning instinct? A theory of
emerging hierarchical models will have to be developed (that is, adaptive,
dynamic, fuzzy hierarchy- heterarchy).

Semiotics studies processes of codification in nature
(Peirce 1935-66; Taborsky, 1999); classical semiotics studied the
symbol-content of culture (Sebeok 1995). This paper concentrates on processes
in the mind that mediate between sensory data and concepts. For example,
consider a written word "chair". It can be interpreted by a mind to
refer to something else: an entity in the world, a specific chair, or the
concept "chair" in the mind. In this process, the mind, or an
intelligent system is called aninterpreter, the written word is called a sign, the real-world chair is called a designatum, and the concept in the
interpreter's mind, the internal representation of the results of
interpretation is called an interpretant
of the sign. The essence of a sign is that it can be interpreted by an
interpreter to refer to something else, a designatum. This process of sign interpretation
is an element of a more general process called semiosis, which consists of
multiple processes of sign interpretation at multiple levels of the mind
hierarchy.

In mathematics and in “Symbolic AI” there is no
difference between signs and symbols. Both are considered as notations,
arbitrary non-adaptive entities with axiomatically fixed meaning. But in
general culture, symbols are understood also as psychological processes of sign
interpretation. Jung emphasized that symbol-processes connect conscious and
unconscious (Jung 1969), Pribram wrote of symbols as adaptive,
context-sensitive signals in the brain, whereas signs he identified with less
adaptive and relatively context-insensitive neural signals (Pribram 1971).

In classical and natural semiotics (Peirce 1935-66;
Sebeok 1995, Morris 1971) the words sign
and symbol are not used consistently;
in this paper, a sign means something that can be interpreted to mean something
else (like a mathematical notation, or a word), and the process of
interpretation is called a symbol-process, or symbol. Interpretation, or
understanding of a sign by the mind according to MFT is due to the fact that a
sign (e.g., a word) is a part of an object-model (or a situation-model at
higher levels of the mind hierarchy). The mechanism of a sign interpretation
therefore involves first an activation of an object-model, which is connected
to instincts that the object might satisfy, and also to behavioral models that
can make use of this object for instinct satisfaction. Second, a sign is
understood in the context of a more general situation in the next layer
consisting of more general concept-models, which accepts as input-signals the
results of lower-level sign recognition. That is, recognized signs comprise
input signals for the next layer models, which ‘cognize’ more general concept-models.

A symbol-process of a sign interpretation coincides
with an elementary thought-process. Each sign-interpretation or elementary
thought process, a symbol, involves conscious and unconscious, emotions,
concepts, and behavior; this definition connecting symbols to archetypes (fuzzy
unconscious model-concepts) corresponds to a usage in general culture and
psychology. As described previously, this process continues up and up the
hierarchy of models and mind toward the most general models. In semiotics this
process is called semiosis, a continuous
process of creating and interpreting the world outside (and inside our mind) as
an infinite hierarchical stream of signs and symbol-processes.

References

Albus, J. and A. Meystel. 2001. Engineering of the Mind:
An Introduction to the Science of Intelligent Systems. New York: Wiley